在线学习适应度地形特征的高效差分演化算法研究及应用

On the basis of understanding the operating mechanism of the evolutionary algorithm and the characteristics of the problem solving, how to adaptively realize the matching of the operation mechanism of the algorithm and the feature of the problem solving, which is not only the key of the theoretical research in the field of evolutionary computation, but also the key to the efficient solution and application of the evolutionary algorithm. For this phenomenon, the analysis method based on the fitness of fitness is one of the hot topics in the field of evolutionary computation in recent years. However, much remains to be done for the online learning landscape characteristics studies in the field of continuous optimization. Therefore, this project takes the differential evolution algorithm as an example. Based on the comprehensive literature review, we summarize a series of research questions for differential evolutionary algorithm, which are presented as follows. (1) From the theoretical aspect: how to analyze the relationships between running mechanism of differential evolutionary and landscape characteristics. (2) From the algorithm design aspect: how to design adaptive differential evolutionary algorithms by online learning landscape characteristics. (3) From extension and application aspect: how to apply the proposed algorithm to the energy saving optimization problem of high speed train tracking operation. At the theoretical level, we use self-organizing map, stochastic differential equation and fitness landscape metrics to analyze and depict the relationship between the adaptive learning mechanism of differential evolution algorithm and fitness landscape features, which lays the foundation for the whole work. At the level of algorithm implementation, it is targeted to design adaptive methods by online comprehensive learning fitness landscape features driven by the relationships, which is an important guarantee for efficient differential evolution algorithm. At the level of popularization and application, the feasibility and effectiveness of the above-mentioned adaptive fitness landscape features in the engineering field are studied. The implementation of this project could enhance the optimization performance and application scope of adaptive differential evolution algorithm, and also plays an active role in expanding and deepening the theory and application of the research field of evolutionary computing.

如何在理解演化算法的运行机制和求解问题特征的基础上，自适应地实现算法的运行机制和求解问题特征的匹配，不仅是演化计算领域理论研究的关键，而且是演化算法高效求解和推广应用的关键。针对此现象，基于适应度地形特征的分析方法是近年来演化计算领域关注的热点之一。然而，在连续优化领域，适应度地形特征的在线学习方法的研究体系尚远未完备。有鉴于此，本项目以差分演化算法为范例，在理论基础层面，利用自组织映射、随机微分方程以及适应度地形度量指标来分析与刻画差分演化算法的自适应学习机制与求解问题适应度地形特征的关联关系，以奠定整个工作的基础；在算法实现层面，以算法与问题的关联关系为驱动，针对性地设计在线综合学习适应度地形特征的自适应方法，是实现高效差分演化算法的重要保障；在推广应用层面，研究上述在线学习适应度地形特征在工程领域应用的可行性与有效性。研究成果对丰富演化计算的理论与方法体系，具有积极的推动作用。

本项目以经典的差分演化算法为范例，研究其运行机制与求解问题特征之间的自适应匹配机理。完成了差分演化算法的自适应学习机制与求解问题适应度地形特征之间的关联关系分析。基于此关联关系理论，设计了在线学习适应度地形特征的自适应方法，并将其应用于列车节能等各类实际优化问题。具体研究工作总结如下：.（1）理论基础层面：利用随机微分方程建立差分演化算法的动力学模型，并引入基于序列的确定性方法对待优化问题的适应度地形特征进行分析，以此实现待优化问题的适应度地形特征与差分演化算法自适应搜索之间关联关系；.（2）算法设计层面：提出三种适应度地形特征驱动的差分演化算法，包括基于随机排序的多模多目标差分演化算法、多因子迁移学习的多模多目标差分演化算法以及自适应协方差学习模型驱动的多目标混合差分-分布估计算法，大量的数值实验验证了提出方法的有效性；.（3）推广应用层面：提出的自适应差分演化算法应用于列车的节能运行操作优化、路侧单元部署优化以及多无人机协同航迹规划优化等实际问题。.在以上三个方面研究进展的基础上，课题组在研究期内发表SCI、EI检索论文10篇，申请发明专利10项，协助培养6名硕士研究生，对照立项时制定的预期目标，已全面保质保量完成。